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physics
modern physics

Physics 5th edition James S. Walker - Solutions

When a beam of atoms emerges from an oven at the absolute temperature T, the most probable de Broglie wavelength for a given atom isIn this expression, m is the mass of an atom, and k is Boltzmann's constant. What is the most probable speed of a hydrogen atom emerging from an oven at 450 K?
Robert A. Millikan (1868- 1953), although best known for his "oil-drop experiment," which measured the charge of an electron, also performed pioneering research on the photoelectric effect. In experiments on lithium, for example, Millikan observed a maximum kinetic energy of 0.550 eV when electrons
A jar is filled with monatomic helium gas at a temperature of 25 °C. The pressure inside the jar is one atmosphere; that is, 101 kPa.(a) Find the average de Broglie wavelength of the helium atoms.(b) Calculate the average separation between helium atoms in the jar. (The fact that the spacing
The Compton wavelength, (C, of a particle of mass m is defined as follows: (C = h/mc.(a) Calculate the Compton wavelength of a proton.(b) Calculate the energy of a photon that has the same wavelength as found in part (a).(c) Show, in general, that a photon with a wavelength equal to the Compton
Light of Frequency 8.22 ×1014 Hz ejects electrons from surface A with a maximum kinetic energy that is 2.00 × 10-19 J greater than the maximum kinetic energy of electrons ejected from surface B. (a) If the frequency of the light is increased, does the difference in maximum kinetic energy observed
At a typical vent temperature of 350 °C, what's the peak frequency of the radiation emitted by the vent, assuming the vent is a blackbody?a. 1.68 × 108 Hzb. 4.53 × 1012 Hzc. 2.06 × 1013 Hzd. 3.66 × 1013 Hz
In which region of the electromagnetic spectrum is the peak frequency of the radiation emitted by the vent in the previous problem? a. Ultraviolet b. Visible c. Infrared d. Microwave
Rhodopsin is most sensitive to light with a vacuum wavelength of 500 nm. Does this light have a higher, lower, or the same frequency as the peak frequency of the vent radiation?
Do you expect the light given off by (a) a neon sign or (b) an incandescent lightbulb to be continuous in distribution or in the form of a line spectrum? Explain.
(a) In the quantum mechanical model of the hydrogen atom, there is one value of n for which the angular momentum of the electron must be zero. What is this value of n?(b) Can the angular momentum of the electron be zero in states with other values of n? Explain.
The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10-11 m from the nucleus, which has a diameter of about 1.0 × 10-15 m. If you assume the hydrogen atom to be a sphere of radius 5.3 × 10-11 m, what fraction of its volume is occupied by the nucleus?
Find (a) the longest wavelength in the Lyman series and (b) the shortest wavelength in the Paschen series.
(a) If the mass of the electron were magically doubled, would the ionization energy of hydrogen increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The ionization energy would increase because the increased mass would mean the electron would orbit
Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 2; (B) singly ionized helium in the state n = 1; (C) doubly ionized lithium in the state n = 3. Rank these three atoms in order of increasing Bohr radius. Indicate ties where appropriate.
Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 3; (B) singly ionized helium in the state n = 2; (C) doubly ionized lithium in the state n = 1. Rank these three atoms in order of increasing energy. Indicate ties where appropriate.
An electron in the n = 1 Bohr orbit has the kinetic energy K1. In terms of K1, what is the kinetic energy of an electron in the n = 2 Bohr orbit?
Find the ratio v/c for an electron in the first excited state (n = 2) of hydrogen.
Find the magnitude of the force exerted on an electron in the ground-state orbit of the Bohr model.
How much energy is required to ionize hydrogen when it is in the n = 3 state?
Find the energy of the photon required to excite a hydrogen atom from the n = 1 state to the n = 4 state.
The global standard for time is based on a transition in cesium atoms that occurs when a microwave photon of frequency 9,192,631,770 Hz is absorbed. What is the energy difference in eV between the two levels of cesium that correspond with this transition?
Referring to Problem 1, suppose the nucleus of the hydrogen atom were enlarged to the size of a baseball (diameter = 7.3 cm). At what typical distance from the center of the baseball would you expect to find the electron?Problem 1The electron in a hydrogen atom is typically found at a distance of
A hydrogen atom is in its second excited state, n = 3. Using the Bohr model of hydrogen, find (a) the linear momentum and (b) the angular momentum of the electron in this atom.
Referring to Problem 20, find (a) The kinetic energy of the electron, (b) The potential energy of the atom, and (c) The total energy of the atom. Give your results in eV.Problem 20A hydrogen atom is in its second excited state, n = 3. Using the Bohr model of hydrogen, find (a) the
Initially, an electron is in the n = 2 state of hydrogen. If this electron acquires an additional 2.86 eV of energy, what is the value of n in the final state of the electron?
Identify the initial and final states if an electron in hydrogen emits a photon with a wavelength of 656 nm.
An electron in hydrogen absorbs a photon and jumps to a higher orbit.(a) Find the energy the photon must have if the initial state is n = 3 and the final state is n = 5.(b) If the initial state was n = 5 and the final state n = 7, would the energy of the photon be greater than, less than, or the
Consider the following four transitions in a hydrogen atom:(i) ni = 2, nf = 6(ii) ni = 2, nf = 8(iii) ni = 7, nf = 8(iv) ni = 6, nf = 2Find (a) The longest- and (b) The shortest-wavelength photon that can be emitted or absorbed by these transitions. Give the value of the wavelength in
Muonium is a hydrogen-like atom in which the electron is replaced with a muon, a fundamental particle with a charge of -e and a mass equal to 207me. (The muon is sometimes referred to loosely as a "heavy electron.")(a) What is the Bohr radius of muonium?(b) Will the wavelengths in the Balmer series
(a) Find the radius of the n = 4 Bohr orbit of a doubly ionized lithium atom (Li2+, Z = 3).(b) Is the energy required to raise an electron from the n = 4 state to the n = 5 state in Li2+ greater than, less than, or equal to the energy required to raise an electron in hydrogen from the n = 4 state
Applying the Bohr model to a triply ionized beryllium atom (Be3+, Z = 4), find (a) The shortest wavelength of the Lyman series for Be3+ and (b) The ionization energy required to remove the final electron in Be3+ .
(a) Calculate the time required for an electron in the n = 2 state of hydrogen to complete one orbit about the nucleus. (b) The typical "lifetime" of an electron in the n = 2 state is roughly 10-8 s- after this time the electron is likely to have dropped back to the n = 1 state. Estimate the
In the Thomson model of the atom, the mass of an atom is distributed uniformly throughout its volume in a material analogous to pudding. (a) Calculate the density of the "pudding" of a gold atom that has a mass of 3.27 × 10-25 kg, modeling it as a sphere of radius 0.144 nm. (b) Compare the
The kinetic energy of an electron in a particular Bohr orbit of hydrogen is 1.35 × 10-19 J. (a) Which Bohr orbit does the electron occupy? (b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the kinetic energy of the electron increase, decrease, or stay the
The potential energy of a hydrogen atom in a particular Bohr orbit is -1.20 × 10-19 J. (a) Which Bohr orbit does the electron occupy in this atom?(b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the potential energy of the atom increase, decrease, or
Consider a head-on collision between two hydrogen atoms, both initially in their ground state and moving with the same aspeed. Find the minimum speed necessary to leave both atoms in their n = 4 state after the collision.
A hydrogen atom is in the initial state ni = n, where n > 1. (a) Find the frequency of the photon that is emitted when the electron jumps to state nf = n - 1. (b) Find the frequency of the electron's orbital motion in the state n. (c) Compare your results for parts (a) and (b) in the limit of
(a) Is the de Broglie wavelength of an electron in the n = 2 Bohr orbit of hydrogen greater than, less than, or equal to the de Broglie wavelength in the n = 1 Bohr orbit? (b) Choose the best explanation from among the following: I. The de Broglie wavelength in the nth state is 2πr > n, where r is
Find the de Broglie wavelength of an electron in the ground state of the hydrogen atom.
The de Broglie wavelength of an electron in a hydrogen atom is 1.66 nm. Identify the integer n that corresponds to its orbit.
The orbital radius of an electron in a hydrogen atom is 0.846 nm. What is its de Broglie wavelength?
Find an expression, in terms of n and the fundamental constants, for the de Broglie wavelength of an electron in the nth state of the hydrogen atom.
What is the radius of the hydrogen-atom Bohr orbit shown in FIGURE 31-40?Figure 31-40
Copper atoms have 29 protons in their nuclei. If the copper nucleus is a sphere with a diameter of 4.8 × 10-15 m, find the work required to bring an alpha particle (charge = +2e) from rest at infinity to the "surface" of the nucleus.
(a) An electron in a hydrogen atom jumps from the n = 6 orbit to the n = 2 orbit and emits a photon. Will its de Broglie wavelength increase, decrease, or stay the same after the jump?(b) Calculate its de Broglie wavelength before and after the jump.
(a) Find the kinetic energy (in eV) of an electron whose de Broglie wavelength is equal to 0.5 Å = 0.05 nm, a typical atomic size.(b) If the wavelength of the electron is reduced to 10–15 m, a typical nuclear size, is its kinetic energy greater than, less than, or equal to the value found in
What are the allowed values of ℓ when the principal quantum number is n = 5?
How many different values of mℓ are possible when the principal quantum number is n = 5?
Give the value of the quantum number ℓ, if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of (a) √6(h/2π), (b) √15(h/2π),(c) √30(h/2π), or (d) √36(h/2π).
Hydrogen atom number 1 is known to be in the 4ƒ state.(a) What is the energy of this atom?(b) What is the magnitude of this atom's orbital angular momentum?(c) Hydrogen atom number 2 is in the 5d state. Is this atom's energy greater than, less than, or the same as that of atom 1? Explain.(d) Is
An electron in a hydrogen atom makes a transition from a 5p state to a 4d state.(a) Does the energy of the electron increase, decrease, or stay the same? Explain.(b) Does the magnitude of the electron's angular momentum increase, decrease, or stay the same? Explain.(c) Calculate the change in the
A hydrogen atom has an orbital angular momentum with a magnitude of 10√57(h/2π).(a) Determine the value of the quantum number ℓ for this atom.(b) What is the minimum possible value of this atom's principal quantum number, n? Explain.(c) If 10√57(h/2π) is the maximum orbital angular momentum
The electron in a hydrogen atom with an energy of -0.544 eV is in a subshell with 18 states.(a) What is the principal quantum number, n, for this atom?(b) What is the maximum possible orbital angular momentum this atom can have?(c) Is the number of states in the subshell with the next lowest value
Consider two different states of a hydrogen atom. In state I the maximum value of the magnetic quantum number is mℓ = 3; in state II the corresponding maximum value is mℓ = 2. Let LI and LII represent the magnitudes of the orbital angular momentum of an electron in states I and II,
In Rutherford's scattering experiments, alpha particles (charge = +2e) were fired at a gold foil. Consider an alpha particle with an initial kinetic energy K heading directly for the nucleus of a gold atom (charge = +79e). The alpha particle will come to rest when all its initial kinetic energy has
How many electrons can occupy(a) The 2p subshell and(b) The 3p subshell?
(a) How many electrons can occupy the 3d subshell?(b) How many electrons can occupy the n = 2 shell?
The electronic configuration of a given atom is 1s22s22p63s23p1. How many electrons are in this atom?
Give the electronic configuration for the ground state of carbon.
Give a list of all possible sets of the four quantum numbers (n, ℓ, mℓ, ms) for electrons in the 3p subshell.
List the values of the four quantum numbers (n, ℓ, mℓ, ms) for each of the electrons in the ground state of neon.
List the values of the four quantum numbers (n, ℓ, mℓ, ms) for each of the electrons in the ground state of magnesium.
The configuration of the outer electrons in Ni is 3d8 4s2. Write out the complete electronic configuration for Ni.
Determine the number of different sets of quantum numbers possible for each of the following shells:(a) n = 2,(b) n = 3,(c) n = 4.
(a) In an X-ray tube, do you expect the wavelength of the characteristic X-rays to increase, decrease, or stay the same if the energy of the electrons striking the target is increased? (b) Choose the best explanation from among the following: I. Increasing the energy of the incoming electrons will
Find the wavelength of the Balmer series spectral line corresponding to n = 12.
Using the Bohr model, estimate the wavelength of the Ka X-ray in nickel (Z = 28).
Using the Bohr model, estimate the energy of a Ka X-ray emitted by lead (Z = 82).
The K-shell ionization energy of iron is 8500 eV, and its L-shell ionization energy is 2125 eV. What is the wavelength of Ka X-rays emitted by iron?
An electron drops from the L shell to the K shell and gives off an X-ray with a wavelength of 0.0279 nm. What is the atomic number of this atom?
Consider an X-ray tube that uses platinum (Z = 78) as its target. (a) Use the Bohr model to estimate the minimum kinetic energy electrons must have in order for Ka X-rays to just appear in the X-ray spectrum of the tube. (b) Assuming the electrons are accelerated from rest through a voltage V,
A person's vision may be improved significantly by having the cornea reshaped with a laser beam, in a procedure known as photorefractive keratectomy. The excimer laser used in these treatments produces ultraviolet light with a wavelength of 193 nm.(a) What is the difference in energy between the
An ultraviolet photon is absorbed by a fluorescent molecule, which then emits two photons.(a) Are the wavelengths of the emitted photons longer than, shorter than, or the same as the wavelength of the ultraviolet photon? Explain.(b) If the ultraviolet photon has a wavelength of 254 nm and one of
The most common fluorescent lightbulb converts ultraviolet light from mercury atoms to white light. If an ultraviolet photon of wavelength 185 nm is emitted by a mercury atom and absorbed by the phosphor, what is the maximum number of red 655-nm photons that the phosphor can emit?
Consider the following three transitions in a hydrogen atom: (A) ni = 5, nf = 2; (B) ni = 7, nf = 2; (C) ni = 7, nf = 6. Rank the transitions in order of increasing (a) wavelength and (b) frequency of the emitted photon. Indicate ties where appropriate.
Suppose an electron is in the ground state of hydrogen. (a) What is the highest-energy photon this system can absorb without dissociating the electron from the proton? Explain. (b) What is the lowest-energy photon this system can absorb? Explain.
What is the smallest value of n for which the wavelength of a Balmer series line is less than 400 nm?
The electronic configuration of a particular carbon atom is 1s22s22p13s1. Is this atom in its ground state or in an excited state? Explain.
Do you expect the ionization energy of sodium (Na) to be greater than, less than, or equal to the ionization energy of lithium (Li)? Explain.
Find the minimum frequency a photon must have if it is to ionize the ground state of the hydrogen atom.
The electron in a hydrogen atom makes a transition from the n = 4 state to the n = 2 state, as indicated in FIGURE 31-41.(a) Determine the linear momentum of the photon emitted as a result of this transition.(b) Using your result to part (a), find the recoil speed of the hydrogen atom, assuming it
In laser eye surgery, the laser emits a 1.45- ns pulse focused on a spot that is 32.5 µm in diameter. (a) If the energy contained in the pulse is 2.95 mJ, what is the power per square meter (the irradiance) associated with this beam? (b) Suppose a molecule with a diameter of 0.500 nm is
Consider an electron in the ground-state orbit of the Bohr model of hydrogen. (a) Find the time required for the electron to complete one orbit about the nucleus. (b) Calculate the current (in amperes) corresponding to the electron's motion.
A particular Bohr orbit in a hydrogen atom has a total energy of -0.85 eV. What are (a) the kinetic energy of the electron in this orbit and (b) the electric potential energy of the system?
An ionized atom has only a single electron. The n = 6 Bohr orbit of this electron has a radius of 2.72 × 10-10 m. Find (a) The atomic number Z of this atom and (b) The total energy E of its n = 3 Bohr orbit.
Find the approximate wavelength of Kb X-rays emitted by molybdenum 1Z = 422, and compare your result with Figure 31-27.
Suppose FIGURE 31-42 shows an electron in an atom that is orbiting a nucleus counterclockwise (that is, the charge is moving to the right at the moment pictured in the diagram). The indicated magnetic field has just been turned on from an initial value of zero. (a) Treating the electron as a
Find the wavelength of the three longest-wavelength lines of the Lyman series.
There is no limit to the size a hydrogen atom can attain, provided it is free from disruptive outside influences. In fact, radio astronomers have detected radiation from large, so-called "Rydberg atoms" in the diffuse hydrogen gas of interstellar space. (a) Find the smallest value of n such
In 1896, the American astronomer Edward C. Pickering (1846-1919) discovered an unusual series of spectral lines in light from the hot star Zeta Puppis. After some time, it was determined that these lines are produced by singly ionized helium. In fact, the "Pickering series" is produced when
Consider a particle of mass m, charge q, and constant speed v moving perpendicular to a uniform magnetic field of magnitude B, as shown in Figure 31-42. The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the
Consider a particle of mass m confined in a one-dimensional box of length L. In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length L that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the
Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts? A. 1.49 W B. 5.76 W C. 5.92 W D. 6.07 W
A red krypton laser also emits 1.49 × 1019 photons per second. Is its power output greater than, less than, or equal to the power output of the argon laser in Problem 84?
The energy difference (in eV) between two states of a particular atom is 2.541 eV. What are the type and wavelength of the laser that corresponds to this transition?A. Kr, 647.1 nmB. Ar, 514.5 nmC. Kr, 568.2 nmD. Ar, 488.0 nm
How would the number of photons emitted per second by a yellow Kr laser compare to the number emitted per second by a red Kr laser that has the same power output?A. The yellow Kr laser emits more photons per second.B. The yellow Kr laser emits fewer photons per second.C. The yellow Kr laser emits
Suppose the electron is in a state whose standing wave consists of two wavelengths.(a) Is the wavelength of this standing wave greater than or less than 1.33 × 10-9 m?(b) Find the wavelength of this standing wave.
(a) Which state has a de Broglie wavelength of 3.99 × 10-9 m?(b) What is the Bohr radius of this state?
Find the wavelength of the longest-wavelength lines of the Paschen series.
Different isotopes of a given element have different masses, but they have the same chemical properties. Explain why chemical properties are unaffected by a change of isotope.

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